Answer:
(7/15,−13/5)
Equation Form:
x=7/15,y=−13/5
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Answer:
40 square metres
Step-by-step explanation:
The shaded region is of a triangle, whose area is denoted by: A = (1/2) * b * h, where b is the base and h is the height.
Since the left figure is a square with side lengths 10, we know that the height of the triangle is also 10 metres. The right figure is a rectangle with length 4. Since the total base length of the entire figure is 18 and the base of the square is 10, then the width of the rectangle is 18 - 10 = 8 metres.
This width is also the base of the triangle, so b = 8.
Now plug these values into the equation:
A = (1/2) * b * h
A = (1/2) * 8 * 10 = (1/2) * 80 = 40
The area is 40 square metres.
The missing coordinates of the parallelogram is (m + h, n).
Solution:
Diagonals of the parallelogram bisect each other.
Solve using mid-point formula:
![$\text{Midpoint} =\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right )](https://tex.z-dn.net/?f=%24%5Ctext%7BMidpoint%7D%20%3D%5Cleft%28%20%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%20%5Cfrac%7By_1%2By_2%7D%7B2%7D%5Cright%20%20%29)
Here ![x_1=m, y_1=n, x_2=h, y_2=0](https://tex.z-dn.net/?f=x_1%3Dm%2C%20y_1%3Dn%2C%20x_2%3Dh%2C%20y_2%3D0)
![$=\left( \frac{m+h}{2}, \frac{n+0}{2}\right )](https://tex.z-dn.net/?f=%24%3D%5Cleft%28%20%5Cfrac%7Bm%2Bh%7D%7B2%7D%2C%20%5Cfrac%7Bn%2B0%7D%7B2%7D%5Cright%20%20%29)
![$\text{Midpoint} =\left( \frac{m+h}{2}, \frac{n}{2}\right )](https://tex.z-dn.net/?f=%24%5Ctext%7BMidpoint%7D%20%3D%5Cleft%28%20%5Cfrac%7Bm%2Bh%7D%7B2%7D%2C%20%5Cfrac%7Bn%7D%7B2%7D%5Cright%20%20%29)
<u>To find the missing coordinate:</u>
Let the missing coordinates by x and y.
Here ![x_1=0, y_1=0, x_2=x, y_2=y](https://tex.z-dn.net/?f=x_1%3D0%2C%20y_1%3D0%2C%20x_2%3Dx%2C%20%20y_2%3Dy)
![$\text{Midpoint}=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )](https://tex.z-dn.net/?f=%24%5Ctext%7BMidpoint%7D%3D%5Cleft%28%20%5Cfrac%7B0%2Bx%7D%7B2%7D%2C%20%5Cfrac%7B0%2By%7D%7B2%7D%5Cright%20%20%29)
![$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{0+x}{2}, \frac{0+y}{2}\right )](https://tex.z-dn.net/?f=%24%5Cleft%28%20%5Cfrac%7Bm%2Bh%7D%7B2%7D%2C%20%5Cfrac%7Bn%7D%7B2%7D%5Cright%20%20%29%3D%5Cleft%28%20%5Cfrac%7B0%2Bx%7D%7B2%7D%2C%20%5Cfrac%7B0%2By%7D%7B2%7D%5Cright%20%20%29)
![$\left( \frac{m+h}{2}, \frac{n}{2}\right )=\left( \frac{x}{2}, \frac{y}{2}\right )](https://tex.z-dn.net/?f=%24%5Cleft%28%20%5Cfrac%7Bm%2Bh%7D%7B2%7D%2C%20%5Cfrac%7Bn%7D%7B2%7D%5Cright%20%20%29%3D%5Cleft%28%20%5Cfrac%7Bx%7D%7B2%7D%2C%20%5Cfrac%7By%7D%7B2%7D%5Cright%20%20%29)
Now equate the x-coordinate.
![$ \frac{m+h}{2}=\frac{x}{2}](https://tex.z-dn.net/?f=%24%20%5Cfrac%7Bm%2Bh%7D%7B2%7D%3D%5Cfrac%7Bx%7D%7B2%7D)
Multiply by 2 on both sides of the equation, we get
m + h = x
x = m + h
Now equate the y-coordinate.
![$\frac{n}{2} = \frac{y}{2}](https://tex.z-dn.net/?f=%24%5Cfrac%7Bn%7D%7B2%7D%20%3D%20%20%5Cfrac%7By%7D%7B2%7D)
Multiply by 2 on both sides of the equation, we get
n = y
y = n
Hence the missing coordinates of the parallelogram is (m + h, n).
The answer to your question is 10 2/5
Answer:
m=![\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D)
Step-by-step explanation: